Large q expansion of the 2D q-states Potts model

Details Large q expansion of the 2D q-states Potts model Large q expansion of the 2D q-states Potts model

1996-01-18

arxiv.org/abs/hep-lat/9601012v1

J.Phys.I(France) 7 (1997) 81-103

Physics

High Energy Physics

High Energy Physics - Lattice

31 pages (tex) including 15 figures (Postscript)

Scientific paper

10.1051/jp1:1997127

We present a recursive method to calculate a large q expansion of the 2d q-states Potts model free energies based on the Fortuin-Kasteleyn representation of the model. With this procedure, we compute directly the ordered phase partition function up to order 10 in 1/sqrt{q}. The energy cumulants at the transition can be obtained with suitable resummation and come out large for q less or around 15. As a consequence, expansions of the free energies around the transition temperature are useless for not large enough values of q. In particular the pure phase specific heats are predicted to be much larger, at q < 15, than the values extracted from current finite size scaling analysis of extrema, whereas they agree very well with recent values extracted at the transition point.

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